Newtons 3rd law - how can this rope move?

Hi I'm having trouble understanding this situation. Appologies if I posted in the wrong place, this is pretty simple but it's not really a homework question.

A horse is attached to a large stone by means of a rope (modelled as light and inextensible). Let the mass of the horse be m and the mass of the boulder be m'. The horse applies a force (on itself) and the system begins to accelerate. As I see it, the forces involved are as follows (ignoring any resistive forces):
The is a force of F on the system, causing it to accelerate according to F=(m+m')a.
The forces on the horse are F and a tension from the rope, say Ft, so the resultant is F-Ft=ma.
The force on the boulder must be from the tension in the rope, so Ft'=m'a.
The rope acts on both the horse and the boulder so a reaction force from both of these acts on the rope, so there are two forces on the rope in opposite directions, and force on rope is equal to Ft-Ft'.

It can be shown algebraiclally and is consistent with the model of tension in a rope that I am familiar with that Ft=Ft'. So my question is how can the rope accelerate if there is no resultant force acting on it?

Thanks:)